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Ryan O’Neill

Michael Reilly

Michael Wu

Helmholtz Resonators

Ever wonder what the use of something like a Helmholtz resonator has in everyday life.

Helmholtz resonators are around us in many different things. hey are in audio e!ui"ment#

instruments# and architectural acoustics. hese things hel" use am"lify sound# make $eautiful

music# and eliminate undesira$le sounds in a room.

One of the most common uses of Helmholtz resonators is in su$woofers. %u$woofers are

a key "art in "roducing low fre!uencies in surround sound systems# concerts# and nightclu$s# &ust

to name a few. %u$woofers were first develo"ed in the '()*s to add $ass res"onse to home

stereo systems. here are different ty"es of su$woofers that use different designs to accom"lish

the same "ur"ose. hese include $ass refle+# infinite $affle# horn,loaded# and $and "ass# all of

these designs have there own advantages and disadvantages.

Helmholtz resonance is also crucial in stringed instruments. -uitars and violins are

Helmholtz resonators that use the vi$rations of the resonator along with vi$rations of the wood

 $odies.

%ome more traditional instruments that are Helmholtz resonators are the ancient ocarina

and the frican d&em$e. he ocarina is an ancient flute,like# wind instrument. /t was most often

ceramic# $ut other materials such as "lastic# wood# and metal have $een used. /t has four to

twelve finger holes on the $ody and a mouth tu$e that "ro&ects outward. he ocarina is different

from the flute in the fact that its tone does not rely on the length of the "i"e# $ut rather the ratio

of the surface area of the o"ened whole and the cu$ic volume within the instrument. he d&em$e

is a hard drum "layed with $are hands. /t was develo"ed in West frica and the instrument is

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thought to $e a$out 0*** years old. he d&em$e also has metal rings on it and comes in different

sizes that will "roduce very different sounds. he sha"e of the d&em$e’s $ody makes a

Helmholtz resonator and gives it a dee" $ass note.

nother use of Helmholtz resonators is in architectural acoustics. hey are used to

reduce undesira$le sounds. his is done $y $uilding a resonator tuned to the same fre!uency as

the undesira$le tone. his is usually used for low fre!uency sounds. common use of this is to

cut down on disru"ting sounds in $uildings.

hese are &ust a few of the many uses for Helmholtz resonators in our everyday lives.

Resonators were even used during ancient times as instruments. hey are also very hel"ful in

 "roducing music and cutting down on annoying noises.

s learned in class# a Helmholtz resonator "roduces sound fre!uencies $y a method

analogous to the oscillation of a mass,s"ring oscillator. /n order for sounds to $e "roduced# the

resonator must contain a neck# as well as a cavity containing a larger volume of air connected to

the neck. he larger volume of air acts as the s"ring. When air is forced into this cavity# e.g.

 $lowing across the o"ening in the neck# the "ressure or air in the cavity is increased. Now that

the "ressure in the cavity is greater than the atmos"heric "ressure outside# the system will

com"ensate in order to reach e!uili$rium and air will $e "ushed out. However# since $y $lowing

across the o"ening in the neck of the resonator causes the "lug of air in the neck to gain some

momentum# the cavity of air will overcom"ensate and e+"el more air out of the resonator than

necessary. Hence# the "ressure inside the resonator will now $e smaller than the "ressure

outside# and in order to com"ensate for the "ressure differences# more air will $e sucked into the

cavity. his "rocess re"eats until the system finally reaches e!uili$rium. 1asically# the

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movement of air into and out of the resonator is identical to the movement of a s"ring along the

vertical a+is.

 Image courtesy of http://www.phys.unsw.edu.au/jw/Helmholtz.html 

s can $e seen in the diagrams a$ove# the neck of air is forced down when the neck of the $ottle

is $lown on thus com"ressing the larger volume of air.

/n class# the formula was given as the e!uation to calculate the

fre!uency of a resonator given the area of the neck# the length of the neck# the volume of air

inside the large cavity# and the s"eed of sound which is generally c 2 03* m4s. his formula was

derived from the resonant fre!uency e!uation which is # where the new

constants γ  and m re"resent the ratio of s"ecific heats and m is the mass of air inside the neck.

%ince volume is the "roduct of area and height# A can $e written as V/L to give

hen# knowing that density ρ 2 m 4 V # ' 4 ρ 2 V 4 m so the e!uation can now

 $e written as %ince the velocity of a gas can $e written as and

knowing that # we can rewrite the e!uation to the familiar form5

Our Helmholtz contra"tion was $uilt $y assem$ling 6 7* oz 8oca,8ola $ottles# one r$or 

Mist 9ine Wine $ottle# and 7 7,liter 8oca,8ola $ottles together. We measured the diameter of the

o"enings# and the length of the necks to calculate the volume of air needed :how much water to

http://www.phys.unsw.edu.au/jw/Helmholtz.htmlhttp://www.phys.unsw.edu.au/jw/Helmholtz.html

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add; to "roduce the fre!uency desired. We then fine tuned the system $y using audacity.

/ncluded are 7 s"ectrums for 80 and

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Works 8ited

Helmholtz Resonator

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